According to a result due to B.T. Polyak, a mapping between Hilbert spaces, which is C1,1 around a regular point, carries a ball centered at that point to a convex set, provided that the radius of the ball is small enough. The present paper considers the extension of such result to mappings defined on a certain subclass of uniformly convex Banach spaces. This enables one to extend to such setting a variational principle for constrained optimization problems, already observed in finite dimension, that establishes a convex behavior for proper localizations of them. Further variational consequences are explored.
Uderzo, A. (2013). On the Polyak convexity principle and its application to variational analysis. NONLINEAR ANALYSIS, 91, 60-71 [10.1016/j.na.2013.06.009].
On the Polyak convexity principle and its application to variational analysis
UDERZO, AMOS
2013
Abstract
According to a result due to B.T. Polyak, a mapping between Hilbert spaces, which is C1,1 around a regular point, carries a ball centered at that point to a convex set, provided that the radius of the ball is small enough. The present paper considers the extension of such result to mappings defined on a certain subclass of uniformly convex Banach spaces. This enables one to extend to such setting a variational principle for constrained optimization problems, already observed in finite dimension, that establishes a convex behavior for proper localizations of them. Further variational consequences are explored.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
